Since you can't enter Goron Mines after preforming EMS, you will not be able to obtain the Bombs from Barnes. However, the bombs are still needed in many cases in the rest of the game, and play a vital part in Skipping the Zora Armor. Luckily, there is a way to still obtain the bombs from a different source using the Ooccoo from Lakebed Temple.
Enter Lanayru Province Early and before unblocking the ice at Zora's Domain use a Cutscene Dive to enter Lakebed Temple without the Bombs. Obtain Ooccoo inside Lakebed Temple, warp out, and complete the Twilight. Go to Upper Zora's River and defeat the Twilit Messangers by Iza's house. Iza will then invite you in and ask you to help her. Agree, and you will obtain the Lent Bomb Bag. Now simply use Ooccoo Jr. to warp back into Lakebed Temple, and empty your bomb bag so that you can obtain Water Bombs. (For the fastest method to empty the bomb bag, click here.)
Important Note: After you have obtained the bombs, instead of having to use clever jumps, to skip any remaining stalactites (mainly only an issue encountered on the Wii Version), you can simply pull out a bomb, and use the Gale Boomerang to use it to knock them down.
If you steal the bomb bag from Iza in order to obtain the bombs, it becomes possible to load the bow into the inventory of the "dummy" game file created by preforming the BiT glitch. Once the bomb bag is stolen and BiT is preformed, dying of the Eldin Bridge and respawning in the King Bulblin battle will result in the bow being in your inventory. It is currently unknown why this happens. For additional information on getting the bow, and even the bombs in your BiT inventory, click here.